It is the latest attempt by Obama's team to slow the rise of GOP outside groups that are poised to spend a lot more than their Democratic counterparts in the 2012 elections. Such groups could eliminate Obama's fundraising advantage for his own war chest.

Crossroads is organized under a section of the tax code that allows it to keep its funding sources private. But since the group is spending millions on campaign ads attacking Democrats, it should disclose its donors as traditional campaign committees are required to do, Robert Bauer, the top lawyer for the Obama campaign and the Democratic National Committee, argued in the complaint.

"There has never been any doubt about its true purpose: to elect candidates of its choice to the presidency and Congress," Bauer wrote. "Crossroads has tried to shield its donors -- wealthy individuals, and corporations who may be pursuing special interest agendas that are not in the national interest."

Democrats and open-government types have made similar arguments. Bauer's complaint relies on a recent federal appeals court decision that the FEC should determine the "major purpose" of such groups and treat them accordingly.